It is common to view programs as a combination of logic and control: the logic part de nes what the program must do, the control part { how to do it. The Logic Programming paradigm was developed with the intention of separating the logic from the control. Recently, extensive research has been conducted on automatic generation of control for logic programs. Only a few of these works considered t...

In this paper we describe how a combination of the classical “universal” E-unification and “rigid”E-unification, called “mixed” E-unification, can be used to efficiently handle equality in universal formula semantic tableaux, that are an extension of free variable tableaux.

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of measurement error with unknown variance. In this paper, we study precise sufficie...

We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula—plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-com...

In a number of recent articles Timothy Williamson has built a strong case for the claim that everything necessarily exists. His argument rests on a combination of the derivability of this claim from quantificational logic, with standard modal principles and a robust understanding of the Kripke semantics for quantified modal logic. In this paper I defend a contingentist, non-Meinongian metaphysi...

Even though higher-order calculi for automated theorem proving are rather old, tableau calculi have not been investigated yet. This paper presents two free variable tableau calculi for higher-order logic that use higher-order uniication as the key inference procedure. These calculi diier in the treatment of the substitutional properties of equivalences. The rst calculus is equivalent in deducti...

implements a rst-order theorem prover based on free-variable semantic tableaux. It is complete, sound, and eecient.

does not allow the transmission of an arbitrary channel. In most situations a receiving process k?(k′′).Q can be alpha-converted ahead of communication so that the bound channel k′′ syntactically matches the free channel k′ in the object of the sending process [11]. The exception happens exactly when k′ is free in Q: alpha-conversion becomes impossible (for it would capture the free variable k′...

In this paper, we will present a deenability theorem for rst order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us rst observe that if M is a model of a theory T in a language L, then, clearly, any deenable subset S M (i.e., a subset S = fa j M j = '(a)g deened by some formula ') is invariant under all automorphisms of M. The s...